The moon does not experience weather, so footprints remain for a very long time unless meteorites or solar wind erase them. Although the surface of the moon is composed of mineral rocks which in some places is as fine as dust, footprints do not disappear right away because there is no atmosphere. With no regular wind or rain to erode them, footprints may stay on the moon for millions of years.
The only reasons that footprints may fade or disappear at some point are solar wind or meteorites. The moon often experiences what is called "micrometeorites" -- tiny meteorite particles that hit the surface of the moon at great speed. There is also solar wind, particles from the sun. Scientists believe that the rocks on the surface of the moon erode about 0.04 inches (0.1 centimeters) in 1 million years. So even if footprints on the moon do fade, it will take a very long time to occur.
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